Does Google allow a privacy card that you can control whether an account is connected to it or not? That wouldn't help if someone racked up a ton of charges and Google bills daily, though.
A failure to pay does not extinguish the underlying debt owed. While the US seems pretty dysfunctional (or customer friendly, depending on how you see it) when it comes to collecting on debts, this is not the case globally.
And even in the US, you could presumably easily find all your Google accounts (including personal ones) locked until you pay the outstanding sum. Not something I'd risk, personally.